01-21-2011 Lecture

01-21-2011 Lecture - Solu%onstotheSchrdingerEqua%on E Each...

This preview shows pages 1–7. Sign up to view the full content.

Solu%ons to the Schrödinger Equa%on Each wave function Ψ is a mathematical description of the shape of the standing wave corresponding to the electron An orbital E

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
What is an Orbital? An orbital refers to a wavefunction, Ψ , that describes the standing wave corresponding to the electron. We will consider the lowest energy wave function Ψ 1S that corresponds to the 1S orbtial Ψ 1S
What is an Orbital? The square of the wavefunction ( Ψ 2 ) gives the probability for finding the electron at that point in that orbital Probability = In three dimensions: Probability is spherical ( Ψ 1S ) 2 As r becomes larger, probability becomes very small, but never zero!

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
What is an Orbital? 90% probability r = 2.6a 0 ( Ψ 1S ) 2 The square of the wavefunction ( Ψ 2 ) gives the probability for finding the electron at that point in that orbital Probability = ( Ψ 1S ) 2 Orbital Size
Radial Probability 2 π r = circumference of atom Integrate 4 π r 2 = surface area of sphere at certain distance (r) Surface area is extremely small near the nucleus. a 0 = most probable radius Spherical shells, “like onion,” greatest chance (brightest, R 2 largest) near nucleus, but smaller surface area and volume (4/3) π r 3 near nucleus So radial probability, 4 π r 2 *R 2 ,ends up being greater at a finite distance away from the nucleus (not at the nucleus).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
So, what does the 1s orbital look like? Ψ
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/13/2011 for the course CHEM 101 taught by Professor Fitts during the Fall '08 term at UPenn.

Page1 / 23

01-21-2011 Lecture - Solu%onstotheSchrdingerEqua%on E Each...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online